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Simplifying -5x2 + 40x + -59 = 3x2 + 26x + -35 Reorder the terms: -59 + 40x + -5x2 = 3x2 + 26x + -35 Reorder the terms: -59 + 40x + -5x2 = -35 + 26x + 3x2 Solving -59 + 40x + -5x2 = -35 + 26x + 3x2 Solving for variable 'x'. Reorder the terms: -59 + 35 + 40x + -26x + -5x2 + -3x2 = -35 + 26x + 3x2 + 35 + -26x + -3x2 Combine like terms: -59 + 35 = -24 -24 + 40x + -26x + -5x2 + -3x2 = -35 + 26x + 3x2 + 35 + -26x + -3x2 Combine like terms: 40x + -26x = 14x -24 + 14x + -5x2 + -3x2 = -35 + 26x + 3x2 + 35 + -26x + -3x2 Combine like terms: -5x2 + -3x2 = -8x2 -24 + 14x + -8x2 = -35 + 26x + 3x2 + 35 + -26x + -3x2 Reorder the terms: -24 + 14x + -8x2 = -35 + 35 + 26x + -26x + 3x2 + -3x2 Combine like terms: -35 + 35 = 0 -24 + 14x + -8x2 = 0 + 26x + -26x + 3x2 + -3x2 -24 + 14x + -8x2 = 26x + -26x + 3x2 + -3x2 Combine like terms: 26x + -26x = 0 -24 + 14x + -8x2 = 0 + 3x2 + -3x2 -24 + 14x + -8x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -24 + 14x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 7x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 7x + -4x2)' equal to zero and attempt to solve: Simplifying -12 + 7x + -4x2 = 0 Solving -12 + 7x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3 + -1.75x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -1.75x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -1.75x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1.75x + x2 = 0 + -3 -1.75x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1.75x + x2 = -3 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = -3 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = -3 + 0.765625 Combine like terms: -3 + 0.765625 = -2.234375 0.765625 + -1.75x + x2 = -2.234375 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = -2.234375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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